Topological phases represent different kind of phases that are distinct from trivially disordered phases but cannot be characterized by symmetry breaking.
A particular class of topological phases are symmetry protected topological (SPT) phases, i.e., phases that are only distinct from a trivially disordered phase as long as certain symmetries are preserved.
A well known example of an SPT phase is the antiferromagnetic spin-1 Heisenberg chain.
As predicted by Haldane [1]}, an antiferromagnetic spin chain with integer spins has a gapped ground state with exponentially decaying correlations.
Following Haldane's prediction, Affleck, Kennedy, Lieb, and Tasaki (AKLT) presented model Hamiltonians for which the ground state can be obtained exactly.[2]}
In addition to providing insight to the Haldane conjecture, the AKLT state was later found to exhibit several interesting properties, such as a nonlocal “string order” and spin-\(1/2\)  edge states, which extend also to states within the same phase.[3]}
